New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Study uses machine learning to identify IBD biomarkers from gut microbiota.
problem Identifying biomarkers for Inflammatory Bowel Disease (IBD) from gut microbiota.
method Ensemble feature selection methods (CMIM, FCBF, mRMR, XGBoost) applied to IBD-associated metagenomics dataset.
result XGBoost minimizes microbiota used for IBD diagnosis, improving classification accuracy.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Paper tackles multi-source domain adaptation for regression.
problem Predicting HDL cholesterol levels using gut microbiome data.
method Two-step procedure: 1) Extend a flexible single-source DA algorithm for classification to regression. 2) Augment with ensemble learning for multi-source DA.
result Consistent improvement in HDL cholesterol level prediction performance over existing methods.
We introduce a new method for estimating the support size of an unknown distribution which provably matches the performance bounds of the state-of-the-art techniques in the area and outperforms them in practice. In particular, we present both theoretical and computer simulation results that illustrate the utility and p…
Compositional data have two unique characteristics compared to typical multivariate data: the observed values are nonnegative and their summand is exactly one. To reflect these characteristics, a specific regularized regression model with linear constraints is commonly used. However, linear constraints incur additional…
Tree-based variational inference improves PLN model for hierarchical count data.
problem Limited applicability of PLN model in ecosystems due to lack of hierarchical tree structures.
method Introduced PLN-Tree model integrating structured variational inference techniques.
result Enhanced generative improvements and practical interpretability in microbiome modeling.
This paper addresses measurement errors in high-dimensional compositional data using a log-contrast model calibration approach.
problem Measurement errors in high-dimensional regression models involving compositional covariates.
method Calibration approach for the linear log-contrast model under lenient sparsity conditions.
result Established asymptotic normality of the estimator for inference.
New models found for guts of nearly fibered knots.
problem Characterizing nearly fibered knots topologically.
method Provided three models for the guts of nearly fibered knots.
result Nearly fibered condition can be purely topologically characterized.
Guts determine the leading coefficients of L2-Alexander torsions for 3-manifolds.
problem Determining the leading coefficient of L2-Alexander torsions for 3-manifolds. method Using a new criterion for the convergence of Fuglede-Kadison determinants and the work of Agol and Zhang on guts of 3-manifolds.
result The leading coefficient equals the relative L2-torsion of the guts associated to the cohomology class. Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.
problem Invariants for 3-manifolds with toral boundaries and non-degenerate Thurston norm.
method Constructing an invariant called guts and proving its invariance under sutured decompositions.
result The guts of different homology classes are related by sutured decompositions.
Improves classification of microbiome data using mixture distributions.
problem Challenges in classifying sparse and heterogeneous microbiome count data.
method Distance-based classification using mixture distributions.
result The method outperforms existing distance-based classifiers and machine learning approaches.
Proposes a convex method to estimate GGMs with covariates.
problem Improving conditional independence structure estimation with covariates.
method Convex optimization framework for joint estimation of mean and precision matrix.
result Improved theoretical guarantees and practical utility demonstrated.
For a hyperbolic 3-orbifold with underlying space the 3-sphere, we obtain a lower bound on its volume in the case that it contains an essential 2-suborbifold with underlying space the 2-sphere with four cone points. Our techniques involve computing the guts of the orbifold split along the 2-suborbifold via a …
AI enhances microbiology and microbiome research through machine learning.
problem Understanding microbial life and its impact on health and the environment.
method AI-driven approaches including machine learning and deep learning.
result Transformative role in enhancing microbial life understanding.
We model microbiome interactions as graphs to interpret complex dynamics.
problem Understanding the differences in microbiome profiles between healthy and ill individuals.
method Developed a method to learn low-dimensional graph representations of time-evolving microbiome interactions.
result Extracted graph features that highlight microbes and interactions strongly correlated with clinical diseases.
Machine learning predicts plant phenotypes from soil microbiome data.
problem Predicting plant phenotypes from soil microbiome data.
method Two models (random forest and Bayesian neural network) were used to predict plant phenotypes from soil properties and microbial population density.
result Human decisions and normalization strategies significantly impact model performance.
Let M be a hyperbolic manifold of finite volume which fibers over the circle with fiber a once punctured torus, and let S be an arbitrary incompressible surface in M. We determine the characteristic JSJ-subpair of M-S and show, in particular, that the guts of (M,S) is empty.
Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.
problem Graphical models in high-dimensional data analysis need to handle clustering and sparsity simultaneously.
method MGLasso combines clustering and graph inference through a convex relaxation of k-means and hierarchical clustering. It uses CONESTA for regularization.
result MGLasso improves network interpretability by estimating graphs at multiple scales.
Researchers found the minimum volume of a 3-cusped hyperbolic 3-manifold.
problem Finding the minimum volume of a 3-cusped orientable hyperbolic 3-manifold.
method Using guts in sutured and pared manifolds.
result The volume of a 3-cusped orientable hyperbolic 3-manifold is at least 5.49... = 6 × Catalan's constant.
A new metric evaluates generative models by comparing real and generated samples.
problem Evaluating the quality of generative models.
method Relative Density Ratio (RDR) function, optimization on variational form of φ-divergence.
result The RDR function provides a clear, interpretable, and numerically stable evaluation metric.
Data augmentation improves microbiome disease prediction.
problem Improving predictive models for microbiome data.
method Defined novel data augmentation strategies for simplex-valued data.
result Set new state-of-the-art for disease prediction tasks.
GraphKKE learns fixed-length feature vectors from time-evolving graphs of human microbiome data.
problem Understanding dynamic changes in human microbiome graphs over time.
method Spectral analysis of transfer operators and graph kernels.
result GraphKKE captures temporal changes in human microbiome graphs.
Unified framework combines dependent microbiome tests.
problem Combining dependent microbiome association tests.
method Generalized meta-analysis framework for dependent tests.
result The vanilla Cauchy combination is a special case.
Modified proof for a broader class of links.
problem Recovering twist number and volume bounds.
method Modified proof for a broader class of links.
result Modified proof works for a broader class of links.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
Study handles in sutured manifolds and knots, finding varied handle numbers and unique surfaces.
problem Understanding handle numbers and incompressible Seifert surfaces in sutured manifolds and nearly fibered knots.
method Extending Haken's Theorem, analyzing product annuli and disks, and examining specific knot types.
result Variety of handle numbers and unique incompressible Seifert surfaces in nearly fibered knots.
Microbes are everywhere, including in and on our bodies, and have been shown to play key roles in a variety of prevalent human diseases. Consequently, there has been intense interest in the design of bacteriotherapies or "bugs as drugs," which are communities of bacteria administered to patients for specific therapeuti…
KernelBiome tackles microbiome research by improving predictive performance and interpretability.
problem Challenges in analyzing high-throughput sequencing data, especially in microbiome research.
method KernelBiome is a kernel-based nonparametric regression and classification framework for compositional data, incorporating prior knowledge and capturing complex signals.
result Improved predictive performance compared to state-of-the-art machine learning methods, with two novel quantities for interpretability.
Bayesian model fuses diverse microbiome data types.
problem Challenges in fusing different types of microbiome data.
method Flexible multinomial-Gaussian generative model with variational EM algorithm.
result Inferred latent variables provide common dimensionality reduction and predictive posterior distribution.
Bayesian method for imputing missing values in tensor data.
problem Missing data in multi-way arrays (tensors) in biomedical studies.
method Flexible Bayesian framework with conjugate priors for CP factorization.
result Accurately captures uncertainty in microbiome profiles at missing timepoints.
New model identifies microbial subcommunities robustly, accounting for cross-sample heterogeneity.
problem Inference in LDA is sensitive to the number of subcommunities and often creates artificial ones.
method Incorporates logistic-tree normal (LTN) model into LDA to account for cross-sample heterogeneity.
result Restores robustness of inference and identifies meaningful subcommunities.
PHIBP models complex microbiome data with shared parameters.
problem Complex, sparse count data in microbiome analysis.
method Bayesian nonparametric framework with shared species parameters.
result Flexible multivariate count model with tractable inference.
New models for analyzing microbiome data with interactions.
problem Analyzing compositional data with interactions.
method Exponential family models with generalized score matching.
result Effective estimation methods for compositional data with interactions.
New method for analyzing compositional data, addressing biases in summary statistics.
problem Inadequate effect measures for compositional data, especially in high-dimensionality and sparsity.
method Perturbation-based effect measures, average perturbation effects.
result Proposed estimators efficiently estimate average perturbation effects, outperforming existing techniques.
Scientific investigations that incorporate next generation sequencing involve analyses of high-dimensional data where the need to organize, collate and interpret the outcomes are pressingly important. Currently, data can be collected at the microbiome level leading to the possibility of personalized medicine whereby tr…
Develops a method for estimating networks and covariate associations in compositional data.
problem Estimating network interactions and covariate associations for compositional data.
method Hierarchical Bayesian model with spike-and-slab priors for edge and covariate selection, variational EM for inference.
result The proposed method outperforms existing methods in network recovery accuracy.
PolyILR: A Tree-Structured Orthonormal Decomposition of Compositional Data
problem Representing compositional data with hierarchical structure
method PolyILR: A canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology
result PolyILR yields stable, interpretable features and enables inference at multiscale tree resolution
Generative model for tabular data density regression.
problem Estimating conditional distribution of outcomes given covariates.
method Tree-based flow model for efficient sampling and likelihood evaluation.
result Our method achieves comparable or superior performance with reduced training and sampling costs.
We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…
Convolutional Neural Networks (CNNs) are a popular deep learning architecture widely applied in different domains, in particular in classifying over images, for which the concept of convolution with a filter comes naturally. Unfortunately, the requirement of a distance (or, at least, of a neighbourhood function) in the…
Hierarchical CNNs improve diagnosis of GI diseases from histopathological images.
problem Diagnosing GI diseases from histopathological images is challenging due to heterogeneity and shared features.
method Embedded a class hierarchy into a VGGNet to address the hierarchical structure of GI diseases.
result The hierarchical model achieved better results than a flat model for multi-category diagnosis of GI disorders.
New ZIPLN model accounts for zero-inflation in multivariate count data.
problem Zero-inflation in multivariate count data.
method Introduced Zero-Inflated PLN (ZIPLN) model with variational inference.
result ZIPLN significantly improves log-likelihood and reduces dispersion.
We prove a finiteness result for the ∂-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a…
We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of the cup …
We construct a class of stable SU(5) bundles on an elliptically fibered Calabi-Yau threefold with two sections, a variant of the ordinary Weierstrass fibration, which admits a free involution. The bundles are invariant under the involution, solve the topological constraint imposed by the heterotic anomaly equation and …
In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c2(X)=c2(V) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explic…
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.